CIMAS - Criterion Impact MeAsurement System

1. 1. Compute expert weights from years of experience.

   $$W^{E_i}=\frac{E_i}{{\sum }_{i=1}^q{E}_i},i=1,2,\dots ,q$$

2. 2. Normalize input data matrix column-wise over experts (linear-sum normalization).

   $$x_{ij}^{\ast }=\frac{x_{ij}}{{\sum }_{i=1}^q{x}_{ij}},i=1,\dots ,q;j=1,\dots ,p$$

3. 3. Multiply each row of the normalized matrix by that expert's weight to obtain the expert-weighted matrix.

   $${\widehat{x^{\ast }}}_{ij}=x_{ij}^{\ast }\cdot W^{E_i}$$

4. 4. Identify the maximum R_j_max and minimum R_j_min of each criterion column in the expert-weighted matrix.

   $$R_{jmax}=\underset{i}{\max }{\widehat{x^{\ast }}}_{ij};R_{jmin}=\underset{i}{\min }{\widehat{x^{\ast }}}_{ij},j=1,\dots ,p$$

5. 5. Compute the difference B_j between R_j_max and R_j_min per criterion.

   $$B_j=R_{jmax}-R_{jmin},j=1,\dots ,p$$

6. 6. Apply the final ranking equation to obtain the criterion importance (weight) L_j by normalizing B_j to sum to 1.

   $$L_j=\frac{B_j}{{\sum }_{j=1}^p{B}_j},j=1,\dots ,p$$